Turbine Nozzle Airfoil Profile

ABSTRACT

The present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

FIELD

The present application relates generally to a turbine nozzle for a gas turbine engine, and more particularly relates to a turbine nozzle airfoil profile for a turbine nozzle.

BACKGROUND

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., stator vanes or nozzles and rotor blades.) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages are set forth below in the following description, or may be obvious from the description, or may be learned through practice.

The present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.

The present application further provides a turbine nozzle including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete suction-side airfoil shape. The X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

The present application further provides a turbine with a number of turbine nozzles having an airfoil having an airfoil shape. The airfoils having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete airfoil shape.

Those of ordinary skill in the art will better appreciate the features and aspects of such embodiments, and others, upon review of the specification.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including the best mode thereof to one skilled in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including alternating rows of turbine rotor blades and turbine nozzles according to at least one embodiment of the present disclosure;

FIG. 2 is a perspective view of an exemplary turbine nozzle according to at least one embodiment of the present disclosure; and

FIG. 3 provides a cross-sectional view of an airfoil portion of the turbine nozzle of FIG. 2.

DETAILED DESCRIPTION

Referring now to the drawings, particularly to FIG. 1, there is illustrated an exemplary turbine 10 of a gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of turbine nozzles or vanes disposed axially adjacent to a corresponding row of turbine rotor blades. Four stages are illustrated in FIG. 1. The exact number of stages of the turbine 10 is a choice of engineering design, and may be more or less than the four stages illustrated in FIG. 1. The four stages are merely exemplary of one turbine design, and are not intended to limit the presently claimed turbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100 and a plurality of turbine rotor blades 150. The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14. The turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14. A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 200 may be coupled to a casing 16 of the turbine 12.

As shown in FIG. 1, a third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 300 may be coupled to the casing 16 of the turbine 12. In particular embodiments, the turbine 12 includes a fourth stage which includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14. The fourth stage turbine nozzles 400 may be coupled to the casing 16 of the turbine 12.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400 and turbine rotor blades 150, 250, 350 and 450 are disposed or at least partially disposed within a hot gas path 18 of the turbine 12. The various stages of the turbine 10 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20, flow during operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine nozzle 50 as may be incorporated in any stage of the turbine 12. FIG. 3 provides a cross-sectional top view of an airfoil 52 of the turbine nozzle 50 shown in FIG. 2. In one embodiment the turbine nozzle 50 as provided in Table I below is representative of turbine nozzle 200 of the plurality of turbine nozzles 200 of the second stage as shown in FIG. 1. As shown in FIGS. 2 and 3 collectively, the turbine nozzle 50 airfoil 52 includes a pressure-side wall 54 and an opposing suction-side wall 56. The pressure-side wall 54 and the suction-side wall 56 meet or intersect at a leading edge 58 and at a trailing edge 60 of the airfoil 52. A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure and suction-side walls 54, 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60.

As shown in FIG. 2, the airfoil 52 includes a root or first end 64 which intersects with and extends radially outwardly from an inner band 66 of the turbine nozzle 50. The airfoil 52 terminates radially at a second end or tip 68 of the airfoil 52. The second end 68 intersects with and extends radially inwardly from an outer band 70 of the turbine nozzle 50. The pressure and suction-side walls 54, 56 can be said to extend in height and/or span or in a span-wise direction 72 between the root 64 and/or the inner band 66 and the second end 68 or the outer band 70. In other words, each turbine nozzle 50 includes an airfoil 52 having opposing pressure and suction-side walls 54, 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58, 60 and that extend in span or span-wise 72 between the root 64 and the second end 68 of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 74 formed between the inner band 66 and the airfoil 52 proximate to the root 64. The fillet 74 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that can reduce fluid dynamic losses as a result of the presence of fillet 74. In particular embodiments, the inner band 66, airfoil 52 and the fillet 74 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered.

The airfoil 52 of the turbine nozzle 50 has a profile at any cross-section taken between the inner band 66 or the root 64 and the second end 68. The X, Y, and Z values are given in Table I as percentage values of the airfoil length or height/span. As one example only, the height or radial span of the airfoil 52 of turbine nozzle 50 may be from about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters). However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.

The gas turbine hot gas path 18 requires airfoils 52 that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each turbine nozzle airfoil 52, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system.

The loci that defines the turbine nozzle airfoil profile includes a set of about 2,200 points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in Table I below defines the profile of the turbine nozzle airfoil at various locations along its length. Table I lists data for a non-coated airfoil. The envelope/tolerance for the coordinates is about +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord 62 in a direction nominal to any airfoil surface location. The point data origin 76 is defined at or proximate to the leading edge 58 of the airfoil 52 and at or proximate to the root 64.

The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units by the values provided in Table I although other units of dimensions may be used when the values are appropriately converted. The X, Y and Z values set forth in Table I are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the height or span of the airfoil 52. As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the leading edge 58 and multiplying by a constant number (e.g., 100). As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the trailing edge 60 and multiplying by a constant number (e.g., 100).

To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table I is multiplied by the Z length of the airfoil in inches. As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis lies generally parallel to the turbine rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward an exhaust end of the turbine 14. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor shaft 14 and the positive Z coordinate value is radially outwardly toward the second end 68 of the airfoil 52. All the values in Table I are given at room temperature and are non-filleted.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section or airfoil shape of the airfoil 52 of the turbine nozzle 50, at each Z distance along the length of the airfoil 52 can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil. As the turbine nozzle surface heats up during operation of the turbine 14, mechanical stresses and elevated temperatures will cause a change in the X, Y and Z values. Accordingly, the values for the profile given in Table I represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil 52. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of +/−5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular turbine nozzle airfoil design and turbine, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Table below at the same temperature. The data is scalable and the geometry pertains to all aerodynamic scales, at above and/or below 3000 RPM. The design of the airfoil 52 of the turbine nozzle 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE I Suction-side Pressure-side X (%) Y (%) Z (%) N X (%) Y (%) Z (%) 0.0000 0.0000 0.0000 1 0.0000 0.0000 0.0000 −0.8148 −1.2328 0.0000 2 0.7046 0.7484 0.0000 −1.3692 −2.6045 0.0000 3 1.5081 1.3892 0.0000 −1.6721 −4.0513 0.0000 4 2.3905 1.9161 0.0000 −1.7497 −5.5294 0.0000 5 3.3304 2.3329 0.0000 −1.6333 −7.0050 0.0000 6 4.3104 2.6446 0.0000 −1.3542 −8.4581 0.0000 7 5.3166 2.8561 0.0000 −0.9374 −9.8786 0.0000 8 6.3379 2.9800 0.0000 −0.4018 −11.2578 0.0000 9 7.3655 3.0225 0.0000 0.2365 −12.5945 0.0000 10 8.3930 2.9925 0.0000 0.9612 −13.8849 0.0000 11 9.4168 2.8974 0.0000 1.7660 −15.1277 0.0000 12 10.4343 2.7422 0.0000 2.6421 −16.3217 0.0000 13 11.4406 2.5282 0.0000 3.5832 −17.4643 0.0000 14 12.4343 2.2666 0.0000 4.5807 −18.5582 0.0000 15 13.4243 1.9837 0.0000 5.6258 −19.6070 0.0000 16 14.4130 1.7009 0.0000 6.7146 −20.6108 0.0000 17 15.4080 1.4393 0.0000 7.8423 −21.5707 0.0000 18 16.4093 1.2065 0.0000 9.0063 −22.4844 0.0000 19 17.4180 1.0025 0.0000 10.2053 −23.3542 0.0000 20 18.4318 0.8298 0.0000 11.4393 −24.1715 0.0000 21 19.4506 0.6859 0.0000 12.7109 −24.9312 0.0000 22 20.4731 0.5732 0.0000 14.0175 −25.6258 0.0000 23 21.4981 0.4919 0.0000 15.3592 −26.2516 0.0000 24 22.5257 0.4418 0.0000 16.7347 −26.8023 0.0000 25 23.5544 0.4243 0.0000 18.1389 −27.2691 0.0000 26 24.5820 0.4406 0.0000 19.5707 −27.6483 0.0000 27 25.6095 0.4894 0.0000 21.0225 −27.9362 0.0000 28 26.6345 0.5732 0.0000 22.4906 −28.1289 0.0000 29 27.6571 0.6896 0.0000 23.9675 −28.2203 0.0000 30 28.6746 0.8398 0.0000 25.4481 −28.2078 0.0000 31 29.6871 1.0250 0.0000 26.9237 −28.0939 0.0000 32 30.6921 1.2441 0.0000 28.3892 −27.8773 0.0000 33 31.6884 1.4969 0.0000 29.8360 −27.5645 0.0000 34 32.6771 1.7822 0.0000 31.2591 −27.1564 0.0000 35 33.6558 2.0989 0.0000 32.6533 −26.6608 0.0000 36 34.6233 2.4468 0.0000 34.0163 −26.0814 0.0000 37 35.5807 2.8235 0.0000 35.3442 −25.4255 0.0000 38 36.5257 3.2303 0.0000 36.6345 −24.6996 0.0000 39 37.4568 3.6658 0.0000 37.8861 −23.9099 0.0000 40 38.3767 4.1264 0.0000 39.1001 −23.0613 0.0000 41 39.2829 4.6145 0.0000 40.2741 −22.1589 0.0000 42 40.1752 5.1264 0.0000 41.4093 −21.2090 0.0000 43 41.0538 5.6608 0.0000 42.5069 −20.2153 0.0000 44 41.9174 6.2190 0.0000 43.5682 −19.1827 0.0000 45 42.7685 6.7972 0.0000 44.5932 −18.1139 0.0000 46 43.6045 7.3967 0.0000 45.5832 −17.0138 0.0000 47 44.4268 8.0138 0.0000 46.5394 −15.8824 0.0000 48 45.2353 8.6496 0.0000 47.4631 −14.7259 0.0000 49 46.0313 9.3016 0.0000 48.3567 −13.5444 0.0000 50 46.8123 9.9700 0.0000 49.2203 −12.3417 0.0000 51 47.5820 10.6533 0.0000 50.0563 −11.1202 0.0000 52 48.3379 11.3517 0.0000 50.8673 −9.8811 0.0000 53 49.0801 12.0626 0.0000 51.6558 −8.6270 0.0000 54 49.8110 12.7860 0.0000 52.4218 −7.3605 0.0000 55 50.5307 13.5219 0.0000 53.1677 −6.0814 0.0000 56 51.2378 14.2691 0.0000 53.8961 −4.7922 0.0000 57 51.9337 15.0263 0.0000 54.6070 −3.4931 0.0000 58 52.6183 15.7947 0.0000 55.3004 −2.1852 0.0000 59 53.2916 16.5720 0.0000 55.9787 −0.8686 0.0000 60 53.9549 17.3579 0.0000 56.6421 0.4543 0.0000 61 54.6070 18.1527 0.0000 57.2929 1.7847 0.0000 62 55.2503 18.9562 0.0000 57.9312 3.1214 0.0000 63 55.8824 19.7685 0.0000 58.5569 4.4631 0.0000 64 56.5056 20.5870 0.0000 59.1727 5.8098 0.0000 65 57.1189 21.4118 0.0000 59.7785 7.1602 0.0000 66 57.7247 22.2441 0.0000 60.3742 8.5169 0.0000 67 58.3204 23.0814 0.0000 60.9612 9.8761 0.0000 68 58.9086 23.9262 0.0000 61.5382 11.2390 0.0000 69 59.4894 24.7747 0.0000 62.1076 12.6070 0.0000 70 60.0613 25.6295 0.0000 62.6683 13.9775 0.0000 71 60.6258 26.4894 0.0000 63.2215 15.3504 0.0000 72 61.1840 27.3542 0.0000 63.7685 16.7272 0.0000 73 61.7334 28.2240 0.0000 64.3079 18.1051 0.0000 74 62.2753 29.0976 0.0000 64.8411 19.4869 0.0000 75 62.8123 29.9762 0.0000 65.3680 20.8711 0.0000 76 63.3404 30.8573 0.0000 65.8886 22.2566 0.0000 77 63.8636 31.7434 0.0000 66.4043 23.6446 0.0000 78 64.3792 32.6345 0.0000 66.9149 25.0350 0.0000 79 64.8886 33.5269 0.0000 67.4193 26.4268 0.0000 80 65.3930 34.4243 0.0000 67.9199 27.8210 0.0000 81 65.8911 35.3242 0.0000 68.4143 29.2165 0.0000 82 66.3830 36.2278 0.0000 68.9049 30.6133 0.0000 83 66.8698 37.1339 0.0000 69.3905 32.0125 0.0000 84 67.3504 38.0426 0.0000 69.8711 33.4130 0.0000 85 67.8273 38.9549 0.0000 70.3479 34.8148 0.0000 86 68.2979 39.8698 0.0000 70.8198 36.2178 0.0000 87 68.7635 40.7872 0.0000 71.2891 37.6220 0.0000 88 69.2240 41.7059 0.0000 71.7547 39.0288 0.0000 89 69.6796 42.6283 0.0000 72.2153 40.4355 0.0000 90 70.1314 43.5532 0.0000 72.4305 41.0951 0.0000 91 70.3417 43.9862 0.0000 72.6446 41.7547 0.0000 92 70.5507 44.4205 0.0000 72.8586 42.4143 0.0000 93 70.7584 44.8548 0.0000 73.0713 43.0751 0.0000 94 70.9650 45.2904 0.0000 73.2841 43.7347 0.0000 95 71.1652 45.7284 0.0000 73.4956 44.3955 0.0000 96 71.3742 46.1627 0.0000 73.7059 45.0563 0.0000 97 71.6621 46.5457 0.0000 73.8023 45.7359 0.0000 98 72.0676 46.8010 0.0000 73.5507 46.3742 0.0000 99 72.5394 46.8861 0.0000 73.0088 46.7935 0.0000 100 73.0088 46.7935 0.0000 −0.8235 0.1915 10.0000 1 −0.8235 0.1915 10.0000 −1.6471 −1.0501 10.0000 2 −0.1114 0.9437 10.0000 −2.2028 −2.4330 10.0000 3 0.7009 1.5845 10.0000 −2.5006 −3.8949 10.0000 4 1.5920 2.1101 10.0000 −2.5695 −5.3842 10.0000 5 2.5407 2.5232 10.0000 −2.4418 −6.8711 10.0000 6 3.5294 2.8310 10.0000 −2.1502 −8.3342 10.0000 7 4.5444 3.0388 10.0000 −1.7184 −9.7635 10.0000 8 5.5732 3.1564 10.0000 −1.1677 −11.1502 10.0000 9 6.6083 3.1940 10.0000 −0.5156 −12.4931 10.0000 10 7.6433 3.1589 10.0000 0.2240 −13.7897 10.0000 11 8.6733 3.0588 10.0000 1.0438 −15.0363 10.0000 12 9.6971 2.8986 10.0000 1.9349 −16.2340 10.0000 13 10.7096 2.6796 10.0000 2.8899 −17.3817 10.0000 14 11.7096 2.4130 10.0000 3.9024 −18.4793 10.0000 15 12.7059 2.1277 10.0000 4.9599 −19.5319 10.0000 16 13.7021 1.8436 10.0000 6.0588 −20.5419 10.0000 17 14.7034 1.5807 10.0000 7.1977 −21.5081 10.0000 18 15.7121 1.3467 10.0000 8.3717 −22.4305 10.0000 19 16.7284 1.1414 10.0000 9.5782 −23.3091 10.0000 20 17.7484 0.9662 10.0000 10.8210 −24.1364 10.0000 21 18.7735 0.8198 10.0000 12.1001 −24.9061 10.0000 22 19.8035 0.7034 10.0000 13.4143 −25.6145 10.0000 23 20.8348 0.6183 10.0000 14.7622 −26.2553 10.0000 24 21.8698 0.5645 10.0000 16.1427 −26.8210 10.0000 25 22.9049 0.5419 10.0000 17.5544 −27.3054 10.0000 26 23.9412 0.5532 10.0000 18.9937 −27.7046 10.0000 27 24.9762 0.5982 10.0000 20.4543 −28.0138 10.0000 28 26.0088 0.6758 10.0000 21.9312 −28.2278 10.0000 29 27.0388 0.7885 10.0000 23.4193 −28.3417 10.0000 30 28.0638 0.9337 10.0000 24.9111 −28.3529 10.0000 31 29.0839 1.1126 10.0000 26.4018 −28.2603 10.0000 32 30.0976 1.3279 10.0000 27.8811 −28.0663 10.0000 33 31.1026 1.5757 10.0000 29.3454 −27.7722 10.0000 34 32.0989 1.8573 10.0000 30.7860 −27.3830 10.0000 35 33.0864 2.1702 10.0000 32.1990 −26.9011 10.0000 36 34.0638 2.5144 10.0000 33.5795 −26.3354 10.0000 37 35.0300 2.8886 10.0000 34.9262 −25.6896 10.0000 38 35.9837 3.2916 10.0000 36.2340 −24.9712 10.0000 39 36.9249 3.7247 10.0000 37.5031 −24.1852 10.0000 40 37.8523 4.1840 10.0000 38.7322 −23.3392 10.0000 41 38.7672 4.6708 10.0000 39.9224 −22.4368 10.0000 42 39.6683 5.1815 10.0000 41.0713 −21.4831 10.0000 43 40.5544 5.7171 10.0000 42.1802 −20.4844 10.0000 44 41.4268 6.2753 10.0000 43.2516 −19.4443 10.0000 45 42.2854 6.8548 10.0000 44.2854 −18.3680 10.0000 46 43.1289 7.4556 10.0000 45.2829 −17.2566 10.0000 47 43.9599 8.0751 10.0000 46.2441 −16.1151 10.0000 48 44.7747 8.7134 10.0000 47.1727 −14.9462 10.0000 49 45.5770 9.3680 10.0000 48.0676 −13.7509 10.0000 50 46.3655 10.0401 10.0000 48.9324 −12.5344 10.0000 51 47.1402 10.7272 10.0000 49.7685 −11.2979 10.0000 52 47.9024 11.4293 10.0000 50.5795 −10.0438 10.0000 53 48.6508 12.1452 10.0000 51.3667 −8.7760 10.0000 54 49.3880 12.8736 10.0000 52.1314 −7.4944 10.0000 55 50.1114 13.6145 10.0000 52.8773 −6.2003 10.0000 56 50.8235 14.3655 10.0000 53.6045 −4.8961 10.0000 57 51.5244 15.1289 10.0000 54.3141 −3.5832 10.0000 58 52.2128 15.9024 10.0000 55.0063 −2.2603 10.0000 59 52.8911 16.6859 10.0000 55.6834 −0.9299 10.0000 60 53.5569 17.4781 10.0000 56.3454 0.4080 10.0000 61 54.2128 18.2804 10.0000 56.9937 1.7534 10.0000 62 54.8586 19.0901 10.0000 57.6295 3.1039 10.0000 63 55.4944 19.9086 10.0000 58.2553 4.4593 10.0000 64 56.1189 20.7347 10.0000 58.8686 5.8198 10.0000 65 56.7359 21.5670 10.0000 59.4731 7.1852 10.0000 66 57.3429 22.4055 10.0000 60.0676 8.5544 10.0000 67 57.9412 23.2516 10.0000 60.6521 9.9287 10.0000 68 58.5307 24.1026 10.0000 61.2278 11.3054 10.0000 69 59.1126 24.9599 10.0000 61.7947 12.6871 10.0000 70 59.6871 25.8223 10.0000 62.3542 14.0713 10.0000 71 60.2528 26.6896 10.0000 62.9061 15.4581 10.0000 72 60.8110 27.5620 10.0000 63.4506 16.8486 10.0000 73 61.3617 28.4393 10.0000 63.9875 18.2416 10.0000 74 61.9049 29.3204 10.0000 64.5194 19.6358 10.0000 75 62.4418 30.2065 10.0000 65.0451 21.0338 10.0000 76 62.9712 31.0976 10.0000 65.5645 22.4330 10.0000 77 63.4944 31.9912 10.0000 66.0788 23.8348 10.0000 78 64.0100 32.8899 10.0000 66.5882 25.2378 10.0000 79 64.5194 33.7910 10.0000 67.0914 26.6433 10.0000 80 65.0238 34.6959 10.0000 67.5895 28.0513 10.0000 81 65.5219 35.6045 10.0000 68.0826 29.4593 10.0000 82 66.0138 36.5156 10.0000 68.5720 30.8711 10.0000 83 66.5006 37.4305 10.0000 69.0551 32.2829 10.0000 84 66.9812 38.3467 10.0000 69.5344 33.6971 10.0000 85 67.4568 39.2678 10.0000 70.0100 35.1114 10.0000 86 67.9274 40.1902 10.0000 70.4819 36.5282 10.0000 87 68.3930 41.1164 10.0000 70.9499 37.9462 10.0000 88 68.8523 42.0438 10.0000 71.4130 39.3655 10.0000 89 69.3079 42.9737 10.0000 71.8736 40.7847 10.0000 90 69.7597 43.9061 10.0000 72.0876 41.4506 10.0000 91 69.9687 44.3442 10.0000 72.3016 42.1164 10.0000 92 70.1777 44.7822 10.0000 72.5144 42.7822 10.0000 93 70.3855 45.2203 10.0000 72.7272 43.4493 10.0000 94 70.5920 45.6596 10.0000 72.9387 44.1151 10.0000 95 70.7922 46.1014 10.0000 73.1502 44.7822 10.0000 96 71.0013 46.5394 10.0000 73.3605 45.4493 10.0000 97 71.2891 46.9262 10.0000 73.4556 46.1352 10.0000 98 71.6959 47.1852 10.0000 73.1977 46.7747 10.0000 99 72.1702 47.2766 10.0000 72.6446 47.1890 10.0000 100 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51.7434 16.3054 30.0000 54.7184 −2.1890 30.0000 59 52.4330 17.1076 30.0000 55.4018 −0.8273 30.0000 60 53.1114 17.9186 30.0000 56.0688 0.5432 30.0000 61 53.7785 18.7397 30.0000 56.7222 1.9199 30.0000 62 54.4343 19.5682 30.0000 57.3617 3.3029 30.0000 63 55.0788 20.4068 30.0000 57.9912 4.6909 30.0000 64 55.7146 21.2516 30.0000 58.6095 6.0826 30.0000 65 56.3392 22.1051 30.0000 59.2165 7.4806 30.0000 66 56.9549 22.9650 30.0000 59.8135 8.8824 30.0000 67 57.5607 23.8310 30.0000 60.4005 10.2879 30.0000 68 58.1589 24.7034 30.0000 60.9800 11.6984 30.0000 69 58.7472 25.5820 30.0000 61.5494 13.1114 30.0000 70 59.3279 26.4656 30.0000 62.1101 14.5282 30.0000 71 59.8999 27.3542 30.0000 62.6633 15.9474 30.0000 72 60.4643 28.2491 30.0000 63.2090 17.3705 30.0000 73 61.0200 29.1477 30.0000 63.7484 18.7960 30.0000 74 61.5695 30.0526 30.0000 64.2804 20.2228 30.0000 75 62.1101 30.9612 30.0000 64.8073 21.6533 30.0000 76 62.6446 31.8736 30.0000 65.3279 23.0851 30.0000 77 63.1715 32.7897 30.0000 65.8423 24.5194 30.0000 78 63.6909 33.7109 30.0000 66.3504 25.9562 30.0000 79 64.2040 34.6358 30.0000 66.8536 27.3942 30.0000 80 64.7121 35.5632 30.0000 67.3517 28.8348 30.0000 81 65.2128 36.4944 30.0000 67.8448 30.2766 30.0000 82 65.7071 37.4293 30.0000 68.3317 31.7196 30.0000 83 66.1965 38.3667 30.0000 68.8148 33.1652 30.0000 84 66.6796 39.3066 30.0000 69.2929 34.6120 30.0000 85 67.1577 40.2503 30.0000 69.7672 36.0601 30.0000 86 67.6295 41.1965 30.0000 70.2365 37.5094 30.0000 87 68.0964 42.1452 30.0000 70.7021 38.9599 30.0000 88 68.5582 43.0964 30.0000 71.1627 40.4130 30.0000 89 69.0150 44.0501 30.0000 71.6208 41.8661 30.0000 90 69.4656 45.0063 30.0000 71.8335 42.5469 30.0000 91 69.6746 45.4556 30.0000 72.0463 43.2290 30.0000 92 69.8824 45.9049 30.0000 72.2578 43.9099 30.0000 93 70.0901 46.3554 30.0000 72.4693 44.5920 30.0000 94 70.2966 46.8048 30.0000 72.6796 45.2741 30.0000 95 70.5044 47.2553 30.0000 72.8886 45.9562 30.0000 96 70.7109 47.7046 30.0000 73.0976 46.6395 30.0000 97 70.9900 48.1101 30.0000 73.1977 47.3392 30.0000 98 71.3980 48.3867 30.0000 72.9337 47.9912 30.0000 99 71.8798 48.4894 30.0000 72.3655 48.4093 30.0000 100 72.3655 48.4093 30.0000 −3.2753 0.6783 40.0000 1 −3.2753 0.6783 40.0000 −4.1101 −0.6108 40.0000 2 −2.5407 1.4531 40.0000 −4.6658 −2.0438 40.0000 3 −1.6984 2.1101 40.0000 −4.9474 −3.5544 40.0000 4 −0.7747 2.6458 40.0000 −4.9900 −5.0926 40.0000 5 0.2078 3.0626 40.0000 −4.8298 −6.6220 40.0000 6 1.2315 3.3667 40.0000 −4.5031 −8.1252 40.0000 7 2.2804 3.5670 40.0000 −4.0313 −9.5907 40.0000 8 3.3442 3.6733 40.0000 −3.4380 −11.0100 40.0000 9 4.4118 3.6971 40.0000 −2.7409 −12.3817 40.0000 10 5.4793 3.6471 40.0000 −1.9549 −13.7059 40.0000 11 6.5407 3.5294 40.0000 −1.0901 −14.9775 40.0000 12 7.5932 3.3479 40.0000 −0.1527 −16.1990 40.0000 13 8.6345 3.1076 40.0000 0.8486 −17.3680 40.0000 14 9.6646 2.8248 40.0000 1.9049 −18.4869 40.0000 15 10.6909 2.5257 40.0000 3.0088 −19.5594 40.0000 16 11.7196 2.2378 40.0000 4.1514 −20.5907 40.0000 17 12.7559 1.9787 40.0000 5.3292 −21.5820 40.0000 18 13.7985 1.7459 40.0000 6.5432 −22.5282 40.0000 19 14.8473 1.5382 40.0000 7.7910 −23.4280 40.0000 20 15.8999 1.3579 40.0000 9.0738 −24.2791 40.0000 21 16.9574 1.2065 40.0000 10.3917 −25.0738 40.0000 22 18.0188 1.0851 40.0000 11.7447 −25.8073 40.0000 23 19.0839 0.9925 40.0000 13.1327 −26.4731 40.0000 24 20.1502 0.9324 40.0000 14.5532 −27.0651 40.0000 25 21.2190 0.9036 40.0000 16.0038 −27.5795 40.0000 26 22.2866 0.9074 40.0000 17.4806 −28.0100 40.0000 27 23.3554 0.9449 40.0000 18.9825 −28.3504 40.0000 28 24.4205 1.0150 40.0000 20.5006 −28.5970 40.0000 29 25.4844 1.1189 40.0000 22.0325 −28.7447 40.0000 30 26.5444 1.2566 40.0000 23.5707 −28.7872 40.0000 31 27.5982 1.4305 40.0000 25.1089 −28.7259 40.0000 32 28.6458 1.6395 40.0000 26.6383 −28.5607 40.0000 33 29.6871 1.8824 40.0000 28.1552 −28.2954 40.0000 34 30.7184 2.1577 40.0000 29.6496 −27.9299 40.0000 35 31.7409 2.4681 40.0000 31.1176 −27.4668 40.0000 36 32.7534 2.8110 40.0000 32.5532 −26.9124 40.0000 37 33.7534 3.1852 40.0000 33.9524 −26.2728 40.0000 38 34.7422 3.5907 40.0000 35.3154 −25.5569 40.0000 39 35.7184 4.0263 40.0000 36.6358 −24.7685 40.0000 40 36.6796 4.4906 40.0000 37.9149 −23.9111 40.0000 41 37.6283 4.9837 40.0000 39.1502 −22.9937 40.0000 42 38.5620 5.5019 40.0000 40.3442 −22.0213 40.0000 43 39.4819 6.0463 40.0000 41.4944 −20.9987 40.0000 44 40.3855 6.6158 40.0000 42.6033 −19.9312 40.0000 45 41.2753 7.2078 40.0000 43.6708 −18.8223 40.0000 46 42.1502 7.8210 40.0000 44.6984 −17.6771 40.0000 47 43.0100 8.4556 40.0000 45.6871 −16.4981 40.0000 48 43.8548 9.1101 40.0000 46.6395 −15.2891 40.0000 49 44.6846 9.7835 40.0000 47.5569 −14.0526 40.0000 50 45.4994 10.4743 40.0000 48.4406 −12.7922 40.0000 51 46.3004 11.1815 40.0000 49.2929 −11.5106 40.0000 52 47.0864 11.9049 40.0000 50.1189 −10.2115 40.0000 53 47.8598 12.6433 40.0000 50.9186 −8.8974 40.0000 54 48.6183 13.3942 40.0000 51.6971 −7.5695 40.0000 55 49.3642 14.1589 40.0000 52.4556 −6.2303 40.0000 56 50.0976 14.9374 40.0000 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32.2829 40.0000 65.2478 23.4168 40.0000 77 63.0325 33.2115 40.0000 65.7622 24.8673 40.0000 78 63.5544 34.1427 40.0000 66.2703 26.3204 40.0000 79 64.0701 35.0788 40.0000 66.7722 27.7747 40.0000 80 64.5795 36.0188 40.0000 67.2691 29.2315 40.0000 81 65.0826 36.9612 40.0000 67.7610 30.6909 40.0000 82 65.5795 37.9074 40.0000 68.2466 32.1514 40.0000 83 66.0701 38.8561 40.0000 68.7284 33.6133 40.0000 84 66.5557 39.8085 40.0000 69.2053 35.0763 40.0000 85 67.0338 40.7635 40.0000 69.6771 36.5419 40.0000 86 67.5081 41.7209 40.0000 70.1439 38.0075 40.0000 87 67.9762 42.6809 40.0000 70.6083 39.4756 40.0000 88 68.4393 43.6446 40.0000 71.0676 40.9449 40.0000 89 68.8974 44.6095 40.0000 71.5219 42.4155 40.0000 90 69.3504 45.5770 40.0000 71.7347 43.1039 40.0000 91 69.5620 46.0313 40.0000 71.9462 43.7935 40.0000 92 69.7710 46.4856 40.0000 72.1564 44.4831 40.0000 93 69.9800 46.9412 40.0000 72.3655 45.1727 40.0000 94 70.1877 47.3955 40.0000 72.5745 45.8636 40.0000 95 70.3930 47.8523 40.0000 72.7835 46.5532 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16 11.1001 2.3429 50.0000 3.5282 −20.7021 50.0000 17 12.1489 2.0839 50.0000 4.7247 −21.6959 50.0000 18 13.2040 1.8498 50.0000 5.9562 −22.6471 50.0000 19 14.2653 1.6446 50.0000 7.2203 −23.5532 50.0000 20 15.3304 1.4643 50.0000 8.5194 −24.4093 50.0000 21 16.4018 1.3129 50.0000 9.8548 −25.2065 50.0000 22 17.4756 1.1915 50.0000 11.2253 −25.9437 50.0000 23 18.5519 1.0989 50.0000 12.6295 −26.6120 50.0000 24 19.6308 1.0375 50.0000 14.0663 −27.2078 50.0000 25 20.7109 1.0088 50.0000 15.5344 −27.7222 50.0000 26 21.7922 1.0125 50.0000 17.0288 −28.1539 50.0000 27 22.8723 1.0488 50.0000 18.5469 −28.4956 50.0000 28 23.9512 1.1202 50.0000 20.0826 −28.7447 50.0000 29 25.0263 1.2253 50.0000 21.6308 −28.8911 50.0000 30 26.0989 1.3642 50.0000 23.1865 −28.9337 50.0000 31 27.1652 1.5382 50.0000 24.7397 −28.8736 50.0000 32 28.2253 1.7459 50.0000 26.2866 −28.7109 50.0000 33 29.2791 1.9900 50.0000 27.8198 −28.4468 50.0000 34 30.3229 2.2678 50.0000 29.3317 −28.0801 50.0000 35 31.3579 2.5795 50.0000 30.8160 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14.3930 50.0000 52.4080 −6.1865 50.0000 56 49.9312 15.1802 50.0000 53.1527 −4.8210 50.0000 57 50.6583 15.9800 50.0000 53.8786 −3.4443 50.0000 58 51.3730 16.7910 50.0000 54.5857 −2.0588 50.0000 59 52.0751 17.6120 50.0000 55.2766 −0.6646 50.0000 60 52.7660 18.4431 50.0000 55.9512 0.7372 50.0000 61 53.4443 19.2854 50.0000 56.6120 2.1452 50.0000 62 54.1126 20.1352 50.0000 57.2591 3.5607 50.0000 63 54.7685 20.9937 50.0000 57.8936 4.9812 50.0000 64 55.4143 21.8611 50.0000 58.5169 6.4068 50.0000 65 56.0488 22.7347 50.0000 59.1289 7.8360 50.0000 66 56.6746 23.6170 50.0000 59.7309 9.2716 50.0000 67 57.2904 24.5056 50.0000 60.3217 10.7109 50.0000 68 57.8961 25.3992 50.0000 60.9036 12.1539 50.0000 69 58.4944 26.3004 50.0000 61.4756 13.6008 50.0000 70 59.0826 27.2078 50.0000 62.0388 15.0513 50.0000 71 59.6621 28.1189 50.0000 62.5932 16.5044 50.0000 72 60.2340 29.0363 50.0000 63.1402 17.9612 50.0000 73 60.7972 29.9599 50.0000 63.6796 19.4205 50.0000 74 61.3517 30.8861 50.0000 64.2128 20.8811 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60.0000 0.6108 −18.7297 60.0000 15 9.4355 2.7159 60.0000 1.7459 −19.8185 60.0000 16 10.4906 2.4293 60.0000 2.9199 −20.8648 60.0000 17 11.5544 2.1715 60.0000 4.1327 −21.8673 60.0000 18 12.6233 1.9399 60.0000 5.3817 −22.8235 60.0000 19 13.6984 1.7359 60.0000 6.6646 −23.7334 60.0000 20 14.7772 1.5569 60.0000 7.9825 −24.5907 60.0000 21 15.8611 1.4068 60.0000 9.3367 −25.3905 60.0000 22 16.9474 1.2854 60.0000 10.7272 −26.1264 60.0000 23 18.0375 1.1940 60.0000 12.1502 −26.7947 60.0000 24 19.1302 1.1339 60.0000 13.6070 −27.3892 60.0000 25 20.2240 1.1064 60.0000 15.0939 −27.9011 60.0000 26 21.3179 1.1114 60.0000 16.6070 −28.3292 60.0000 27 22.4105 1.1502 60.0000 18.1427 −28.6671 60.0000 28 23.5019 1.2215 60.0000 19.6971 −28.9111 60.0000 29 24.5907 1.3267 60.0000 21.2628 −29.0551 60.0000 30 25.6758 1.4668 60.0000 22.8348 −29.0951 60.0000 31 26.7559 1.6421 60.0000 24.4055 −29.0313 60.0000 32 27.8298 1.8536 60.0000 25.9700 −28.8623 60.0000 33 28.8949 2.0989 60.0000 27.5194 −28.5920 60.0000 34 29.9524 2.3792 60.0000 29.0476 −28.2203 60.0000 35 31.0000 2.6946 60.0000 30.5482 −27.7509 60.0000 36 32.0375 3.0426 60.0000 32.0175 −27.1902 60.0000 37 33.0626 3.4230 60.0000 33.4506 −26.5419 60.0000 38 34.0763 3.8348 60.0000 34.8448 −25.8160 60.0000 39 35.0763 4.2778 60.0000 36.1990 −25.0150 60.0000 40 36.0626 4.7509 60.0000 37.5106 −24.1464 60.0000 41 37.0338 5.2528 60.0000 38.7785 −23.2165 60.0000 42 37.9912 5.7822 60.0000 40.0038 −22.2303 60.0000 43 38.9337 6.3379 60.0000 41.1840 −21.1915 60.0000 44 39.8611 6.9186 60.0000 42.3217 −20.1051 60.0000 45 40.7722 7.5244 60.0000 43.4155 −18.9750 60.0000 46 41.6683 8.1514 60.0000 44.4693 −17.8060 60.0000 47 42.5482 8.8010 60.0000 45.4819 −16.6033 60.0000 48 43.4130 9.4718 60.0000 46.4568 −15.3692 60.0000 49 44.2628 10.1615 60.0000 47.3942 −14.1064 60.0000 50 45.0964 10.8686 60.0000 48.2991 −12.8198 60.0000 51 45.9161 11.5932 60.0000 49.1727 −11.5119 60.0000 52 46.7196 12.3354 60.0000 50.0175 −10.1840 60.0000 53 47.5106 13.0914 60.0000 50.8360 −8.8411 60.0000 54 48.2854 13.8636 60.0000 51.6308 −7.4844 60.0000 55 49.0476 14.6483 60.0000 52.4043 −6.1139 60.0000 56 49.7960 15.4456 60.0000 53.1564 −4.7334 60.0000 57 50.5319 16.2553 60.0000 53.8886 −3.3417 60.0000 58 51.2541 17.0776 60.0000 54.6033 −1.9399 60.0000 59 51.9637 17.9099 60.0000 55.3004 −0.5294 60.0000 60 52.6608 18.7522 60.0000 55.9812 0.8886 60.0000 61 53.3467 19.6045 60.0000 56.6471 2.3129 60.0000 62 54.0200 20.4668 60.0000 57.2979 3.7447 60.0000 63 54.6834 21.3379 60.0000 57.9374 5.1815 60.0000 64 55.3342 22.2165 60.0000 58.5645 6.6245 60.0000 65 55.9750 23.1026 60.0000 59.1802 8.0726 60.0000 66 56.6058 23.9962 60.0000 59.7847 9.5244 60.0000 67 57.2265 24.8974 60.0000 60.3780 10.9812 60.0000 68 57.8385 25.8048 60.0000 60.9625 12.4418 60.0000 69 58.4406 26.7171 60.0000 61.5357 13.9061 60.0000 70 59.0350 27.6358 60.0000 62.1014 15.3742 60.0000 71 59.6195 28.5607 60.0000 62.6571 16.8448 60.0000 72 60.1952 29.4906 60.0000 63.2053 18.3191 60.0000 73 60.7622 30.4255 60.0000 63.7459 19.7960 60.0000 74 61.3229 31.3667 60.0000 64.2791 21.2766 60.0000 75 61.8736 32.3104 60.0000 64.8060 22.7584 60.0000 76 62.4180 33.2603 60.0000 65.3254 24.2428 60.0000 77 62.9549 34.2128 60.0000 65.8385 25.7297 60.0000 78 63.4831 35.1702 60.0000 66.3454 27.2190 60.0000 79 64.0063 36.1314 60.0000 66.8461 28.7096 60.0000 80 64.5219 37.0964 60.0000 67.3417 30.2028 60.0000 81 65.0313 38.0651 60.0000 67.8298 31.6984 60.0000 82 65.5332 39.0363 60.0000 68.3141 33.1940 60.0000 83 66.0300 40.0113 60.0000 68.7922 34.6934 60.0000 84 66.5207 40.9887 60.0000 69.2653 36.1927 60.0000 85 67.0063 41.9700 60.0000 69.7334 37.6946 60.0000 86 67.4856 42.9524 60.0000 70.1965 39.1977 60.0000 87 67.9587 43.9387 60.0000 70.6546 40.7021 60.0000 88 68.4268 44.9274 60.0000 71.1089 42.2090 60.0000 89 68.8899 45.9186 60.0000 71.5582 43.7159 60.0000 90 69.3479 46.9124 60.0000 71.7685 44.4218 60.0000 91 69.5607 47.3780 60.0000 71.9762 45.1289 60.0000 92 69.7722 47.8448 60.0000 72.1840 45.8360 60.0000 93 69.9825 48.3116 60.0000 72.3905 46.5432 60.0000 94 70.1927 48.7797 60.0000 72.5970 47.2503 60.0000 95 70.4005 49.2478 60.0000 72.8023 47.9587 60.0000 96 70.6083 49.7171 60.0000 73.0063 48.6658 60.0000 97 70.8786 50.1489 60.0000 73.1227 49.3880 60.0000 98 71.2816 50.4606 60.0000 72.8636 50.0663 60.0000 99 71.7772 50.5795 60.0000 72.2791 50.5006 60.0000 100 72.2791 50.5006 60.0000 −5.6283 0.8223 70.0000 1 −5.6283 0.8223 70.0000 −6.4718 −0.5232 70.0000 2 −4.8786 1.6358 70.0000 −7.0200 −2.0125 70.0000 3 −4.0138 2.3267 70.0000 −7.2841 −3.5782 70.0000 4 −3.0613 2.8899 70.0000 −7.3029 −5.1677 70.0000 5 −2.0451 3.3279 70.0000 −7.1139 −6.7459 70.0000 6 −0.9850 3.6471 70.0000 −6.7509 −8.2929 70.0000 7 0.1026 3.8561 70.0000 −6.2441 −9.7997 70.0000 8 1.2040 3.9687 70.0000 −5.6158 −11.2603 70.0000 9 2.3104 3.9925 70.0000 −4.8811 −12.6708 70.0000 10 3.4168 3.9387 70.0000 −4.0563 −14.0300 70.0000 11 4.5169 3.8148 70.0000 −3.1502 −15.3354 70.0000 12 5.6083 3.6245 70.0000 −2.1690 −16.5882 70.0000 13 6.6871 3.3730 70.0000 −1.1239 −17.7860 70.0000 14 7.7559 3.0839 70.0000 −0.0200 −18.9312 70.0000 15 8.8223 2.7835 70.0000 1.1302 −20.0288 70.0000 16 9.8911 2.4981 70.0000 2.3217 −21.0826 70.0000 17 10.9700 2.2441 70.0000 3.5507 −22.0901 70.0000 18 12.0538 2.0150 70.0000 4.8185 −23.0513 70.0000 19 13.1427 1.8123 70.0000 6.1214 −23.9625 70.0000 20 14.2353 1.6358 70.0000 7.4593 −24.8210 70.0000 21 15.3329 1.4881 70.0000 8.8348 −25.6195 70.0000 22 16.4343 1.3680 70.0000 10.2453 −26.3542 70.0000 23 17.5382 1.2791 70.0000 11.6909 −27.0175 70.0000 24 18.6446 1.2203 70.0000 13.1677 −27.6070 70.0000 25 19.7509 1.1940 70.0000 14.6746 −28.1139 70.0000 26 20.8586 1.2003 70.0000 16.2078 −28.5344 70.0000 27 21.9650 1.2403 70.0000 17.7635 −28.8636 70.0000 28 23.0701 1.3141 70.0000 19.3367 −29.0976 70.0000 29 24.1727 1.4230 70.0000 20.9212 −29.2315 70.0000 30 25.2703 1.5670 70.0000 22.5106 −29.2616 70.0000 31 26.3642 1.7459 70.0000 24.0989 −29.1890 70.0000 32 27.4506 1.9599 70.0000 25.6796 −29.0125 70.0000 33 28.5294 2.2090 70.0000 27.2441 −28.7322 70.0000 34 29.5995 2.4931 70.0000 28.7885 −28.3529 70.0000 35 30.6608 2.8110 70.0000 30.3054 −27.8773 70.0000 36 31.7109 3.1640 70.0000 31.7910 −27.3104 70.0000 37 32.7497 3.5482 70.0000 33.2403 −26.6571 70.0000 38 33.7747 3.9650 70.0000 34.6508 −25.9224 70.0000 39 34.7872 4.4143 70.0000 36.0213 −25.1151 70.0000 40 35.7860 4.8936 70.0000 37.3479 −24.2378 70.0000 41 36.7697 5.4018 70.0000 38.6308 −23.2991 70.0000 42 37.7384 5.9387 70.0000 39.8698 −22.3016 70.0000 43 38.6934 6.5006 70.0000 41.0651 −21.2541 70.0000 44 39.6308 7.0889 70.0000 42.2165 −20.1577 70.0000 45 40.5544 7.7021 70.0000 43.3254 −19.0175 70.0000 46 41.4606 8.3379 70.0000 44.3930 −17.8385 70.0000 47 42.3517 8.9962 70.0000 45.4205 −16.6245 70.0000 48 43.2265 9.6746 70.0000 46.4080 −15.3780 70.0000 49 44.0864 10.3730 70.0000 47.3592 −14.1039 70.0000 50 44.9299 11.0901 70.0000 48.2766 −12.8048 70.0000 51 45.7584 11.8248 70.0000 49.1615 −11.4831 70.0000 52 46.5720 12.5770 70.0000 50.0163 −10.1427 70.0000 53 47.3705 13.3442 70.0000 50.8448 −8.7860 70.0000 54 48.1552 14.1264 70.0000 51.6496 −7.4143 70.0000 55 48.9262 14.9212 70.0000 52.4330 −6.0288 70.0000 56 49.6821 15.7297 70.0000 53.1940 −4.6333 70.0000 57 50.4255 16.5507 70.0000 53.9349 −3.2253 70.0000 58 51.1564 17.3842 70.0000 54.6558 −1.8085 70.0000 59 51.8736 18.2278 70.0000 55.3592 −0.3830 70.0000 60 52.5782 19.0826 70.0000 56.0463 1.0513 70.0000 61 53.2703 19.9474 70.0000 56.7184 2.4931 70.0000 62 53.9499 20.8210 70.0000 57.3755 3.9412 70.0000 63 54.6195 21.7034 70.0000 58.0188 5.3955 70.0000 64 55.2766 22.5945 70.0000 58.6496 6.8561 70.0000 65 55.9237 23.4931 70.0000 59.2691 8.3204 70.0000 66 56.5607 24.3992 70.0000 59.8773 9.7897 70.0000 67 57.1877 25.3129 70.0000 60.4743 11.2641 70.0000 68 57.8048 26.2328 70.0000 61.0601 12.7422 70.0000 69 58.4130 27.1577 70.0000 61.6358 14.2240 70.0000 70 59.0113 28.0901 70.0000 62.2028 15.7109 70.0000 71 59.6020 29.0275 70.0000 62.7610 17.2003 70.0000 72 60.1827 29.9700 70.0000 63.3091 18.6921 70.0000 73 60.7559 30.9174 70.0000 63.8511 20.1877 70.0000 74 61.3191 31.8711 70.0000 64.3842 21.6859 70.0000 75 61.8761 32.8285 70.0000 64.9111 23.1865 70.0000 76 62.4243 33.7910 70.0000 65.4305 24.6896 70.0000 77 62.9650 34.7572 70.0000 65.9437 26.1952 70.0000 78 63.4994 35.7284 70.0000 66.4493 27.7021 70.0000 79 64.0250 36.7021 70.0000 66.9487 29.2115 70.0000 80 64.5457 37.6809 70.0000 67.4431 30.7234 70.0000 81 65.0588 38.6621 70.0000 67.9299 32.2378 70.0000 82 65.5657 39.6471 70.0000 68.4118 33.7534 70.0000 83 66.0663 40.6345 70.0000 68.8874 35.2703 70.0000 84 66.5607 41.6258 70.0000 69.3579 36.7897 70.0000 85 67.0488 42.6195 70.0000 69.8235 38.3104 70.0000 86 67.5319 43.6158 70.0000 70.2841 39.8323 70.0000 87 68.0088 44.6158 70.0000 70.7397 41.3567 70.0000 88 68.4806 45.6183 70.0000 71.1902 42.8811 70.0000 89 68.9474 46.6220 70.0000 71.6370 44.4080 70.0000 90 69.4080 47.6295 70.0000 71.8448 45.1227 70.0000 91 69.6220 48.1014 70.0000 72.0513 45.8385 70.0000 92 69.8360 48.5745 70.0000 72.2578 46.5544 70.0000 93 70.0476 49.0488 70.0000 72.4631 47.2703 70.0000 94 70.2591 49.5219 70.0000 72.6671 47.9875 70.0000 95 70.4681 49.9962 70.0000 72.8698 48.7034 70.0000 96 70.6771 50.4718 70.0000 73.0726 49.4205 70.0000 97 70.9349 50.9199 70.0000 73.1940 50.1502 70.0000 98 71.3429 51.2340 70.0000 72.9387 50.8398 70.0000 99 71.8423 51.3605 70.0000 72.3517 51.2816 70.0000 100 72.3517 51.2816 70.0000 −6.3955 0.7997 80.0000 1 −6.3955 0.7997 80.0000 −7.2403 −0.5632 80.0000 2 −5.6395 1.6283 80.0000 −7.7822 −2.0751 80.0000 3 −4.7722 2.3367 80.0000 −8.0413 −3.6608 80.0000 4 −3.8110 2.9136 80.0000 −8.0513 −5.2666 80.0000 5 −2.7835 3.3617 80.0000 −7.8536 −6.8623 80.0000 6 −1.7109 3.6884 80.0000 −7.4806 −8.4255 80.0000 7 −0.6108 3.9049 80.0000 −6.9625 −9.9474 80.0000 8 0.5044 4.0213 80.0000 −6.3217 −11.4218 80.0000 9 1.6245 4.0476 80.0000 −5.5757 −12.8461 80.0000 10 2.7447 3.9950 80.0000 −4.7384 −14.2178 80.0000 11 3.8598 3.8686 80.0000 −3.8185 −15.5369 80.0000 12 4.9637 3.6721 80.0000 −2.8248 −16.8010 80.0000 13 6.0563 3.4193 80.0000 −1.7647 −18.0100 80.0000 14 7.1389 3.1302 80.0000 −0.6471 −19.1665 80.0000 15 8.2203 2.8323 80.0000 0.5194 −20.2741 80.0000 16 9.3079 2.5569 80.0000 1.7284 −21.3329 80.0000 17 10.4005 2.3054 80.0000 2.9775 −22.3454 80.0000 18 11.4994 2.0788 80.0000 4.2641 −23.3104 80.0000 19 12.6033 1.8786 80.0000 5.5857 −24.2265 80.0000 20 13.7109 1.7034 80.0000 6.9449 −25.0864 80.0000 21 14.8223 1.5582 80.0000 8.3417 −25.8836 80.0000 22 15.9387 1.4406 80.0000 9.7735 −26.6133 80.0000 23 17.0563 1.3542 80.0000 11.2416 −27.2703 80.0000 24 18.1765 1.2991 80.0000 12.7409 −27.8511 80.0000 25 19.2979 1.2753 80.0000 14.2703 −28.3479 80.0000 26 20.4193 1.2841 80.0000 15.8248 −28.7572 80.0000 27 21.5394 1.3279 80.0000 17.4005 −29.0751 80.0000 28 22.6583 1.4055 80.0000 18.9937 −29.2966 80.0000 29 23.7747 1.5169 80.0000 20.5970 −29.4155 80.0000 30 24.8861 1.6646 80.0000 22.2040 −29.4305 80.0000 31 25.9937 1.8461 80.0000 23.8098 −29.3442 80.0000 32 27.0939 2.0638 80.0000 25.4068 −29.1564 80.0000 33 28.1852 2.3179 80.0000 26.9875 −28.8661 80.0000 34 29.2691 2.6083 80.0000 28.5469 −28.4743 80.0000 35 30.3429 2.9312 80.0000 30.0801 −27.9862 80.0000 36 31.4055 3.2891 80.0000 31.5807 −27.4093 80.0000 37 32.4568 3.6796 80.0000 33.0451 −26.7472 80.0000 38 33.4956 4.1014 80.0000 34.4718 −26.0063 80.0000 39 34.5219 4.5569 80.0000 35.8573 −25.1890 80.0000 40 35.5319 5.0426 80.0000 37.2003 −24.3041 80.0000 41 36.5282 5.5582 80.0000 38.4994 −23.3567 80.0000 42 37.5094 6.1026 80.0000 39.7547 −22.3517 80.0000 43 38.4743 6.6733 80.0000 40.9662 −21.2941 80.0000 44 39.4230 7.2716 80.0000 42.1339 −20.1902 80.0000 45 40.3567 7.8936 80.0000 43.2591 −19.0413 80.0000 46 41.2741 8.5382 80.0000 44.3429 −17.8523 80.0000 47 42.1752 9.2053 80.0000 45.3855 −16.6283 80.0000 48 43.0613 9.8936 80.0000 46.3880 −15.3717 80.0000 49 43.9312 10.6020 80.0000 47.3529 −14.0851 80.0000 50 44.7847 11.3279 80.0000 48.2841 −12.7735 80.0000 51 45.6233 12.0726 80.0000 49.1815 −11.4406 80.0000 52 46.4468 12.8348 80.0000 50.0501 −10.0864 80.0000 53 47.2553 13.6120 80.0000 50.8911 −8.7159 80.0000 54 48.0488 14.4055 80.0000 51.7071 −7.3304 80.0000 55 48.8273 15.2115 80.0000 52.5006 −5.9312 80.0000 56 49.5920 16.0325 80.0000 53.2716 −4.5207 80.0000 57 50.3442 16.8648 80.0000 54.0213 −3.0976 80.0000 58 51.0814 17.7096 80.0000 54.7509 −1.6646 80.0000 59 51.8073 18.5657 80.0000 55.4631 −0.2228 80.0000 60 52.5181 19.4318 80.0000 56.1564 1.2278 80.0000 61 53.2190 20.3079 80.0000 56.8335 2.6871 80.0000 62 53.9061 21.1940 80.0000 57.4956 4.1514 80.0000 63 54.5820 22.0889 80.0000 58.1452 5.6233 80.0000 64 55.2466 22.9925 80.0000 58.7810 7.1001 80.0000 65 55.8999 23.9036 80.0000 59.4043 8.5820 80.0000 66 56.5432 24.8235 80.0000 60.0163 10.0701 80.0000 67 57.1765 25.7484 80.0000 60.6158 11.5620 80.0000 68 57.7997 26.6809 80.0000 61.2040 13.0588 80.0000 69 58.4130 27.6195 80.0000 61.7822 14.5594 80.0000 70 59.0175 28.5645 80.0000 62.3504 16.0638 80.0000 71 59.6133 29.5156 80.0000 62.9099 17.5707 80.0000 72 60.1990 30.4718 80.0000 63.4593 19.0826 80.0000 73 60.7772 31.4330 80.0000 64.0013 20.5957 80.0000 74 61.3467 32.3992 80.0000 64.5357 22.1126 80.0000 75 61.9086 33.3692 80.0000 65.0613 23.6320 80.0000 76 62.4618 34.3454 80.0000 65.5807 25.1552 80.0000 77 63.0075 35.3254 80.0000 66.0926 26.6796 80.0000 78 63.5457 36.3091 80.0000 66.5982 28.2053 80.0000 79 64.0776 37.2966 80.0000 67.0964 29.7347 80.0000 80 64.6020 38.2879 80.0000 67.5882 31.2653 80.0000 81 65.1189 39.2829 80.0000 68.0738 32.7985 80.0000 82 65.6308 40.2816 80.0000 68.5532 34.3342 80.0000 83 66.1352 41.2829 80.0000 69.0263 35.8711 80.0000 84 66.6345 42.2866 80.0000 69.4944 37.4093 80.0000 85 67.1277 43.2941 80.0000 69.9562 38.9499 80.0000 86 67.6145 44.3054 80.0000 70.4130 40.4906 80.0000 87 68.0951 45.3179 80.0000 70.8648 42.0338 80.0000 88 68.5707 46.3342 80.0000 71.3129 43.5795 80.0000 89 69.0413 47.3517 80.0000 71.7547 45.1252 80.0000 90 69.5069 48.3730 80.0000 71.9612 45.8498 80.0000 91 69.7222 48.8511 80.0000 72.1652 46.5745 80.0000 92 69.9374 49.3304 80.0000 72.3692 47.3004 80.0000 93 70.1514 49.8110 80.0000 72.5720 48.0250 80.0000 94 70.3642 50.2904 80.0000 72.7747 48.7509 80.0000 95 70.5757 50.7722 80.0000 72.9762 49.4768 80.0000 96 70.7872 51.2528 80.0000 73.1765 50.2028 80.0000 97 71.0388 51.7121 80.0000 73.3041 50.9399 80.0000 98 71.4443 52.0401 80.0000 73.0551 51.6395 80.0000 99 71.9487 52.1715 80.0000 72.4643 52.0914 80.0000 100 72.4643 52.0914 80.0000 −7.1615 0.7134 90.0000 1 −7.1615 0.7134 90.0000 −7.9987 −0.6783 90.0000 2 −6.4080 1.5632 90.0000 −8.5357 −2.2103 90.0000 3 −5.5344 2.2891 90.0000 −8.7847 −3.8160 90.0000 4 −4.5670 2.8836 90.0000 −8.7872 −5.4406 90.0000 5 −3.5307 3.3504 90.0000 −8.5795 −7.0526 90.0000 6 −2.4468 3.6921 90.0000 −8.1965 −8.6333 90.0000 7 −1.3342 3.9212 90.0000 −7.6683 −10.1702 90.0000 8 −0.2040 4.0476 90.0000 −7.0163 −11.6596 90.0000 9 0.9312 4.0814 90.0000 −6.2578 −13.0976 90.0000 10 2.0676 4.0338 90.0000 −5.4068 −14.4844 90.0000 11 3.1977 3.9136 90.0000 −4.4743 −15.8160 90.0000 12 4.3179 3.7247 90.0000 −3.4656 −17.0914 90.0000 13 5.4268 3.4743 90.0000 −2.3917 −18.3116 90.0000 14 6.5269 3.1852 90.0000 −1.2566 −19.4781 90.0000 15 7.6233 2.8874 90.0000 −0.0738 −20.5932 90.0000 16 8.7247 2.6045 90.0000 1.1539 −21.6596 90.0000 17 9.8335 2.3567 90.0000 2.4218 −22.6783 90.0000 18 10.9487 2.1339 90.0000 3.7297 −23.6446 90.0000 19 12.0676 1.9362 90.0000 5.0751 −24.5569 90.0000 20 13.1915 1.7647 90.0000 6.4593 −25.4130 90.0000 21 14.3191 1.6208 90.0000 7.8798 −26.2028 90.0000 22 15.4506 1.5069 90.0000 9.3379 −26.9249 90.0000 23 16.5845 1.4230 90.0000 10.8298 −27.5720 90.0000 24 17.7196 1.3705 90.0000 12.3529 −28.1402 90.0000 25 18.8561 1.3492 90.0000 13.9061 −28.6233 90.0000 26 19.9937 1.3617 90.0000 15.4844 −29.0163 90.0000 27 21.1289 1.4080 90.0000 17.0826 −29.3141 90.0000 28 22.2628 1.4894 90.0000 18.6959 −29.5144 90.0000 29 23.3942 1.6045 90.0000 20.3191 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10.8373 90.0000 47.3817 −14.0150 90.0000 50 44.6783 11.5757 90.0000 48.3292 −12.6934 90.0000 51 45.5269 12.3317 90.0000 49.2428 −11.3479 90.0000 52 46.3605 13.1051 90.0000 50.1252 −9.9825 90.0000 53 47.1777 13.8949 90.0000 50.9800 −8.5982 90.0000 54 47.9800 14.6996 90.0000 51.8098 −7.1990 90.0000 55 48.7685 15.5194 90.0000 52.6145 −5.7860 90.0000 56 49.5432 16.3517 90.0000 53.3967 −4.3605 90.0000 57 50.3029 17.1965 90.0000 54.1577 −2.9237 90.0000 58 51.0501 18.0538 90.0000 54.8986 −1.4756 90.0000 59 51.7822 18.9237 90.0000 55.6195 −0.0175 90.0000 60 52.5031 19.8023 90.0000 56.3217 1.4493 90.0000 61 53.2103 20.6921 90.0000 57.0075 2.9249 90.0000 62 53.9049 21.5920 90.0000 57.6771 4.4068 90.0000 63 54.5882 22.5006 90.0000 58.3329 5.8949 90.0000 64 55.2603 23.4180 90.0000 58.9737 7.3892 90.0000 65 55.9212 24.3429 90.0000 59.6020 8.8899 90.0000 66 56.5720 25.2753 90.0000 60.2178 10.3942 90.0000 67 57.2115 26.2153 90.0000 60.8223 11.9049 90.0000 68 57.8411 27.1615 90.0000 61.4143 13.4193 90.0000 69 58.4618 28.1139 90.0000 61.9950 14.9387 90.0000 70 59.0726 29.0726 90.0000 62.5657 16.4618 90.0000 71 59.6746 30.0375 90.0000 63.1264 17.9887 90.0000 72 60.2666 31.0075 90.0000 63.6783 19.5181 90.0000 73 60.8511 31.9825 90.0000 64.2203 21.0513 90.0000 74 61.4268 32.9637 90.0000 64.7547 22.5882 90.0000 75 61.9937 33.9487 90.0000 65.2816 24.1264 90.0000 76 62.5519 34.9387 90.0000 65.7997 25.6683 90.0000 77 63.1039 35.9324 90.0000 66.3104 27.2115 90.0000 78 63.6483 36.9312 90.0000 66.8148 28.7584 90.0000 79 64.1840 37.9324 90.0000 67.3116 30.3066 90.0000 80 64.7134 38.9387 90.0000 67.8010 31.8573 90.0000 81 65.2365 39.9487 90.0000 68.2841 33.4105 90.0000 82 65.7534 40.9612 90.0000 68.7610 34.9662 90.0000 83 66.2641 41.9775 90.0000 69.2315 36.5232 90.0000 84 66.7672 42.9962 90.0000 69.6971 38.0814 90.0000 85 67.2653 44.0175 90.0000 70.1552 39.6421 90.0000 86 67.7572 45.0426 90.0000 70.6083 41.2028 90.0000 87 68.2441 46.0701 90.0000 71.0563 42.7672 90.0000 88 68.7234 47.1014 90.0000 71.4994 44.3317 90.0000 89 69.1990 48.1339 90.0000 71.9374 45.8986 90.0000 90 69.6683 49.1690 90.0000 72.1414 46.6320 90.0000 91 69.8874 49.6546 90.0000 72.3442 47.3667 90.0000 92 70.1039 50.1414 90.0000 72.5457 48.1014 90.0000 93 70.3204 50.6270 90.0000 72.7459 48.8360 90.0000 94 70.5357 51.1151 90.0000 72.9462 49.5720 90.0000 95 70.7484 51.6020 90.0000 73.1439 50.3066 90.0000 96 70.9612 52.0914 90.0000 73.3417 51.0426 90.0000 97 71.2065 52.5607 90.0000 73.4756 51.7885 90.0000 98 71.6095 52.9036 90.0000 73.2328 52.4994 90.0000 99 72.1189 53.0438 90.0000 72.6408 52.9625 90.0000 100 72.6408 52.9625 90.0000 −7.9274 0.6070 100.0000 1 −7.9274 0.6070 100.0000 −8.7622 −0.8073 100.0000 2 −7.1727 1.4768 100.0000 −9.2891 −2.3642 100.0000 3 −6.2916 2.2190 100.0000 −9.5257 −3.9912 100.0000 4 −5.3129 2.8285 100.0000 −9.5119 −5.6370 100.0000 5 −4.2641 3.3066 100.0000 −9.2879 −7.2666 100.0000 6 −3.1677 3.6596 100.0000 −8.8899 −8.8636 100.0000 7 −2.0401 3.8974 100.0000 −8.3467 −10.4168 100.0000 8 −0.8949 4.0313 100.0000 −7.6796 −11.9212 100.0000 9 0.2578 4.0726 100.0000 −6.9061 −13.3742 100.0000 10 1.4093 4.0300 100.0000 −6.0413 −14.7747 100.0000 11 2.5569 3.9136 100.0000 −5.0951 −16.1202 100.0000 12 3.6946 3.7284 100.0000 −4.0726 −17.4105 100.0000 13 4.8210 3.4806 100.0000 −2.9837 −18.6446 100.0000 14 5.9349 3.1865 100.0000 −1.8348 −19.8235 100.0000 15 7.0501 2.8886 100.0000 −0.6370 −20.9524 100.0000 16 8.1702 2.6195 100.0000 0.6070 −22.0300 100.0000 17 9.2979 2.3767 100.0000 1.8949 −23.0563 100.0000 18 10.4305 2.1589 100.0000 3.2228 −24.0275 100.0000 19 11.5670 1.9662 100.0000 4.5907 −24.9437 100.0000 20 12.7084 1.7997 100.0000 5.9987 −25.7972 100.0000 21 13.8536 1.6608 100.0000 7.4456 −26.5807 100.0000 22 15.0013 1.5519 100.0000 8.9299 −27.2929 100.0000 23 16.1514 1.4731 100.0000 10.4481 −27.9274 100.0000 24 17.3041 1.4268 100.0000 12.0000 −28.4781 100.0000 25 18.4568 1.4118 100.0000 13.5795 −28.9387 100.0000 26 19.6095 1.4318 100.0000 15.1840 −29.3079 100.0000 27 20.7610 1.4844 100.0000 16.8073 −29.5807 100.0000 28 21.9111 1.5720 100.0000 18.4431 −29.7534 100.0000 29 23.0576 1.6946 100.0000 20.0876 −29.8273 100.0000 30 24.2003 1.8523 100.0000 21.7334 −29.7972 100.0000 31 25.3367 2.0463 100.0000 23.3742 −29.6658 100.0000 32 26.4668 2.2766 100.0000 25.0038 −29.4330 100.0000 33 27.5882 2.5432 100.0000 26.6158 −29.0989 100.0000 34 28.7009 2.8461 100.0000 28.2040 −28.6696 100.0000 35 29.8035 3.1827 100.0000 29.7647 −28.1477 100.0000 36 30.8949 3.5544 100.0000 31.2929 −27.5369 100.0000 37 31.9737 3.9612 100.0000 32.7860 −26.8436 100.0000 38 33.0401 4.4005 100.0000 34.2403 −26.0726 100.0000 39 34.0926 4.8723 100.0000 35.6558 −25.2315 100.0000 40 35.1302 5.3755 100.0000 37.0288 −24.3242 100.0000 41 36.1527 5.9086 100.0000 38.3592 −23.3542 100.0000 42 37.1589 6.4718 100.0000 39.6471 −22.3292 100.0000 43 38.1502 7.0613 100.0000 40.8899 −21.2516 100.0000 44 39.1252 7.6771 100.0000 42.0901 −20.1239 100.0000 45 40.0826 8.3179 100.0000 43.2466 −18.9537 100.0000 46 41.0250 8.9837 100.0000 44.3617 −17.7422 100.0000 47 41.9487 9.6733 100.0000 45.4355 −16.4944 100.0000 48 42.8573 10.3830 100.0000 46.4706 −15.2140 100.0000 49 43.7497 11.1139 100.0000 47.4681 −13.9049 100.0000 50 44.6245 11.8648 100.0000 48.4305 −12.5695 100.0000 51 45.4831 12.6345 100.0000 49.3605 −11.2115 100.0000 52 46.3267 13.4205 100.0000 50.2591 −9.8323 100.0000 53 47.1552 14.2228 100.0000 51.1277 −8.4343 100.0000 54 47.9675 15.0413 100.0000 51.9712 −7.0200 100.0000 55 48.7660 15.8736 100.0000 52.7897 −5.5920 100.0000 56 49.5494 16.7196 100.0000 53.5845 −4.1502 100.0000 57 50.3191 17.5782 100.0000 54.3567 −2.6971 100.0000 58 51.0738 18.4493 100.0000 55.1076 −1.2315 100.0000 59 51.8160 19.3317 100.0000 55.8385 0.2428 100.0000 60 52.5457 20.2253 100.0000 56.5507 1.7272 100.0000 61 53.2616 21.1289 100.0000 57.2453 3.2203 100.0000 62 53.9650 22.0426 100.0000 57.9237 4.7196 100.0000 63 54.6571 22.9650 100.0000 58.5857 6.2265 100.0000 64 55.3367 23.8961 100.0000 59.2353 7.7397 100.0000 65 56.0063 24.8360 100.0000 59.8698 9.2578 100.0000 66 56.6646 25.7835 100.0000 60.4919 10.7822 100.0000 67 57.3116 26.7372 100.0000 61.1001 12.3116 100.0000 68 57.9487 27.6984 100.0000 61.6971 13.8461 100.0000 69 58.5770 28.6658 100.0000 62.2829 15.3842 100.0000 70 59.1952 29.6383 100.0000 62.8573 16.9274 100.0000 71 59.8035 30.6183 100.0000 63.4205 18.4743 100.0000 72 60.4030 31.6033 100.0000 63.9750 20.0238 100.0000 73 60.9937 32.5932 100.0000 64.5194 21.5770 100.0000 74 61.5757 33.5895 100.0000 65.0551 23.1339 100.0000 75 62.1502 34.5895 100.0000 65.5832 24.6934 100.0000 76 62.7146 35.5945 100.0000 66.1026 26.2553 100.0000 77 63.2728 36.6033 100.0000 66.6133 27.8198 100.0000 78 63.8223 37.6170 100.0000 67.1164 29.3867 100.0000 79 64.3655 38.6345 100.0000 67.6133 30.9574 100.0000 80 64.9011 39.6558 100.0000 68.1014 32.5294 100.0000 81 65.4305 40.6809 100.0000 68.5832 34.1026 100.0000 82 65.9524 41.7084 100.0000 69.0588 35.6796 100.0000 83 66.4681 42.7397 100.0000 69.5269 37.2578 100.0000 84 66.9775 43.7735 100.0000 69.9887 38.8373 100.0000 85 67.4819 44.8110 100.0000 70.4443 40.4193 100.0000 86 67.9800 45.8511 100.0000 70.8936 42.0025 100.0000 87 68.4706 46.8949 100.0000 71.3379 43.5882 100.0000 88 68.9574 47.9399 100.0000 71.7760 45.1740 100.0000 89 69.4380 48.9887 100.0000 72.2090 46.7622 100.0000 90 69.9124 50.0388 100.0000 72.4105 47.5069 100.0000 91 70.1339 50.5319 100.0000 72.6108 48.2516 100.0000 92 70.3529 51.0263 100.0000 72.8098 48.9962 100.0000 93 70.5720 51.5194 100.0000 73.0075 49.7422 100.0000 94 70.7885 52.0138 100.0000 73.2053 50.4869 100.0000 95 71.0050 52.5094 100.0000 73.4018 51.2328 100.0000 96 71.2203 53.0050 100.0000 73.5970 51.9787 100.0000 97 71.4643 53.4856 100.0000 73.7322 52.7347 100.0000 98 71.8536 53.8523 100.0000 73.4931 53.4568 100.0000 99 72.3667 54.0063 100.0000 72.8974 53.9274 100.0000 100 72.8974 53.9274 100.0000

It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine nozzle will be different than those in Table I and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction between other stages in the turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings. The disclosed loci of points defined in Table I allow the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction between other stages in the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings are maintained in the scaled turbine.

The airfoil 52 described herein thus improves overall gas turbine 12 efficiency. Specifically, the airfoil 52 provides a desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52 also meets all aeromechanics and stress requirements. The turbine nozzle 50 described herein has very specific aerodynamic design requirements such as an upstream bucket radial back pressure (i.e., work splits) and radial velocity triangles for the downstream turbine rotors 150, 250, 350 and 450. Significant cross-functional design effort was require to meet these design goals. The airfoil 52 of the turbine nozzle 50 thus is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost effective manner.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

What is claimed is:
 1. A turbine nozzle comprising an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
 2. The turbine nozzle of claim 1, wherein the turbine nozzle forms part of a stage of a turbine.
 3. The turbine nozzle of claim 1, wherein the turbine nozzle is a second stage turbine nozzle.
 4. The turbine nozzle of claim 1, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 5. The turbine nozzle of claim 1, wherein a height of the turbine nozzle is about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters) in length.
 6. The turbine nozzle of claim 1, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 7. A turbine nozzle comprising a an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 8. The turbine nozzle of claim 7, wherein the turbine nozzle forms part of a stage of a turbine.
 9. The turbine nozzle of claim 7, wherein the turbine nozzle is a second stage turbine nozzle.
 10. The turbine nozzle of claim 7, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 11. The turbine nozzle of claim 7, wherein a height of the turbine nozzle is about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters) in length.
 12. A turbine comprising a plurality of turbine nozzles, each of the turbine nozzles comprising an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
 13. The turbine of claim 12, wherein the plurality of turbine nozzles forms part of a stage of a turbine.
 14. The turbine of claim 12, wherein the plurality of turbine nozzles comprises a plurality of second stage turbine nozzles.
 15. The turbine of claim 12, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 16. The turbine of claim 12, wherein a height the turbine nozzle is about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters) in length.
 17. The turbine of claim 12, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 18. The turbine of claim 12, wherein X represents a distance parallel to a turbine axis of rotation. 